A family F of permutations of the vertices of a hypergraph H is called pairwise suitable for H if, for every pair of disjoint edges in H, there exists a permutation in F in which all the vertices in one edge precede those in the other. The cardinality of a smallest such family of permutations for H is called the separation dimension of H and is denoted by π(H). Equivalently, π(H) is the smallest natural number k so that the vertices of H can be embedded in ℝk such that any two disjoint edges of H can be separated by a hyperplane normal to one of the axes. We show that the separation dimension of a hypergraph H is equal to the boxicity of the line graph of H. This connection helps us in borrowing results and techniques from the extensive literature on boxicity to study the concept of separation dimension.
|Title of host publication||Graph-Theoretic Concepts in Computer Science - 40th International Workshop, WG 2014, Revised Selected Papers|
|Editors||Dieter Kratsch, Ioan Todinca|
|Number of pages||12|
|State||Published - 2014|
|Event||40th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2014 - Orléans, France|
Duration: 25 Jun 2014 → 27 Jun 2014
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||40th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2014|
|Period||25/06/14 → 27/06/14|
Bibliographical noteFunding Information:
Rogers Mathew and Deepak Rajendraprasad: Supported by VATAT Postdoctoral Fellowship, Council of Higher Education, Israel.
Manu Basavaraju: Supported by the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement n. 267959.
© Springer International Publishing Switzerland 2014.
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science (all)